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BECE 1992 - MATHEMATICS [PAPER II]
THEORY QUESTIONS
(a)
Solve 5 – 2x > x + 2, where x is a real number.
Illustrate your result on the number line.
(b)
Find the truth set of the equation:
(c)
Factorize completely: mp + np – mt – nt
(d)
Make t the subject of the relation v = u + at
A landlady rented out her house for ₵240,000.00 for one year. During the year she paid 15% of the rent as income tax. She also paid 25% of the rent as property tax and spent ₵10,000.00 on repairs.
Calculate:
(a)
The landlady's total expenses.
(b)
The remainder of the rent after the landlady's expenses.
(c)
The percentage of the rent she spent on repairs.
(a)
Using a scale of 2 cm to 1 unit on both axes, draw perpendicular lines OX and OY on a graph sheet.
(b)
On this graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6
(c)
Plot on the same graph sheet the points A(1, 1), B(4, 3) and C(2, 5). Join the points A, B and C to form a triangle.
(d)
Using the y-axis as the mirror line, draw the image A1B1C1 of the triangle ABC, such that A→A1, B→B1 and C→C1. Write down the co-ordinates of A1, B1 and C1.
(e)
Using the x-axis as the mirror line, draw the image A2B2C2 of triangle ABC where A→A2, B→B2 and C→C2.
The table below gives the frequency distribution of the marks obtained in a class test by a group of 64 pupils.
| Marks (Out of ten) | Frequency |
| 2 | 9 |
| 3 | 14 |
| 4 | 13 |
| 5 | 10 |
| 6 | 5 |
| 7 | 8 |
| 8 | 2 |
| 9 | 3 |
(a)
Draw a bar chart for the distribution.
(b)
A pupil is chosen at random from the class. What is the probability that the pupil obtained 7 marks?
Using a ruler and a pair of compasses only,
(a)
draw |PQ| = 9 cm
(b)
construct a perpendicular to PQ at Q
(c)
construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm
(d)
construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.